Which of the following numbers is a multiple of 14? ${62,98,100,113,117}$
The multiples of $14$ are $14$ $28$ $42$ $56$ ..... In general, any number that leaves no remainder when divided by $14$ is considered a multiple of $14$ We can start by dividing each of our answer choices by $14$ $62 \div 14 = 4\text{ R }6$ $98 \div 14 = 7$ $100 \div 14 = 7\text{ R }2$ $113 \div 14 = 8\text{ R }1$ $117 \div 14 = 8\text{ R }5$ The only answer choice that leaves no remainder after the division is $98$ $ 7$ $14$ $98$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $98$ $98 = 2\times7\times7 14 = 2\times7$ Therefore the only multiple of $14$ out of our choices is $98$. We can say that $98$ is divisible by $14$.